At power-line frequencies (typically 50 or 60 Hz), the electric and magnetic fields are quasi-static: that is, the separate (static) terms are much larger than the coupled (“EM”) field terms. For example, the magnetic field measured at a sensor location is equal to the superposition of the constituent magnetic fields due to the currents in each line (as reported in Olsen and Wong, “Characteristics of Low Frequency Electric and Magnetic Fields in the Vicinity of Electric Power Lines,” IEEE Transactions on Power Delivery, Vol. 7, No. 4, pp. 2046-2055, October, 1992)). These constituent fields are vector fields that change in time (e.g., at 50/60 Hz), with the sources.
Specifically, the line currents that typically exist on electric power lines give rise to quasi-static magnetic fields according to the Biot-Savart Law (as reported in Jackson, Classical Electrodynamics, 3rd Ed., Chap 5, Wiley, NY, 1999). Similarly, the AC voltages on electric power lines give rise to quasi-static electric fields (see chapter 1 of Classical Electrodynamics). Like the magnetic field, the constituent electric fields are out of phase with each other in time, and so the total electric field is a rotating field. This rotation can be seen, for example, using false-color movies generated by ARL-PLUMS, which is referenced in the publication by David Hull and Ross Adelman entitled “An interactive 2-D Power-Line Modeling and Simulation tool”, Proceedings of SPIE/DSS, Vol. 8382, No. 3, April 2012. However, the sources of the quasi-static electric field are the line charges, not the line voltages. Each of these source charges is a linear function of not only the complex-valued line voltages, but also of the self- and mutual capacitances between the energized lines and any grounded objects. Since the capacitance (per unit length) changes with the line sag, proximity to the poles, and other factors, the electric charge density is not even constant along each line, unlike the line currents that are the source of the magnetic field.
Poly-phase (typically, three-phase) power lines are operated with the voltages 120 degrees out of phase with each other. A complex-valued measurement, called a phasor, is commonly used to describe the magnitude and phase of these sinusoidal voltage functions. If the phase angle is referenced to a common time base, such as can be provided by GPS, then the phasor is called a synchrophasor. Synchrophasors are useful for analyzing the dynamic stability of a power system over a wide area, particularly on a transmission grid. Similarly, the magnitude and phase of electric currents can be described as phasors. In general, the angle between the line current and the corresponding line voltage phasors is not zero; this load phasor angle is described in U.S. Pat. No. 7,701,196. Load phasors are useful for analyzing the dynamic loads on a power system, particularly a distribution network, and for adding or subtracting reactive power (volt-amps reactive, or VARs) to the system to reduce I2R losses or otherwise improve the performance of a power system. Moreover, the angle between the current phasors in a three-phase power system is not always equal to 120 degrees; this can occur, for example, when the three-phase load is not balanced.
Magnetic sensors may be utilized to estimate an unknown wire position (or dynamic wire sag), in addition to estimating rms line currents, using data from an additional magnetic-field sensor (or with three additional sensors for three independent sags). A method for doing this is described in U.S. Pat. No. 8,280,652, issued to Promethean Devices. This patent does not appear to envision the additional complexities involved with electric-field sensing and calibration, and the method used in that patent does not apply when using electric-field sensors.
Magnetic and electric-field sensors may be utilized to estimate the magnitude and direction of net electrical power over a power line. For example, see U.S. Pat. Nos. 6,714,000, 6,771,058, 6,956,364, and 7,088,090 issued to Genscape, Inc. These patents disclose the computation of voltage phasors in situations where the assumptions made with relatively simple 2-D models hold (i.e., away from trees, transmission line structures, and fences).
The present invention relates broadly to the monitoring of power lines and, in particular, to power quality and synchrophasor monitoring on power lines. With the advent of Distributed Generation (DG), electric power grid management increasingly monitors power quality parameters in the grid as reported in G. Benmouyal, et al., “Synchronized phasor measurement in protective relays for protection, control, and analysis of electric power systems,” 57th Annual Conference for Protective Relay Engineers, April 2004, pp. 419-450 and O'Brien, J. et. al., “Use of Synchrophasor Measurements in Protective Relaying Applications”, Power System Relaying Committee, Report of Working Group C-14 of the System Protection Subcommittee, April 2012. Therefore, there is a need for systems that monitor the electrical power grid.